Statistical Science

Prediction of Future Observations in Growth Curve Models

C. Radhakrishna Rao

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Abstract

The problem of predicting a future measurement on an individual given the past measurements is discussed under nonparametric and parametric growth models. The efficiencies of different methods of prediction are assessed by cross-validation or leave-one-out technique in each of three data sets and the results are compared. Under nonparametric models, direct and inverse regression methods of prediction are described and their relative advantages and disadvantages are discussed. Under parametric models polynomial and factor analytic type growth curves are considered. Bayesian and empirical Bayesian methods are used to deal with unknown parameters. A general finding is that much of the information for forecasting is contained in the immediate past few observations or a few summary statistics based on past data. A number of data reduction methods are suggested and analyses based on them are described. The usefulness of the leave-one-out technique in model selection is demonstrated. A new method of calibration is introduced to improve prediction.

Article information

Source
Statist. Sci., Volume 2, Number 4 (1987), 434-447.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177013119

Digital Object Identifier
doi:10.1214/ss/1177013119

Mathematical Reviews number (MathSciNet)
MR933738

Zentralblatt MATH identifier
0955.62551

JSTOR
links.jstor.org

Keywords
Bayesian approach calibration cross-validation empirical Bayes factor analytic model inverse regression leave-one-out method mixed model part correlation polynomial model predictive density principal component regression

Citation

Rao, C. Radhakrishna. Prediction of Future Observations in Growth Curve Models. Statist. Sci. 2 (1987), no. 4, 434--447. doi:10.1214/ss/1177013119. https://projecteuclid.org/euclid.ss/1177013119


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See also

  • See Comment: David R. Brillinger. [Prediction of Future Observations in Growth Curve Models]: Comment. Statist. Sci., Volume 2, Number 4 (1987), 448--450.
  • See Comment: Nan Laird, Nick Lange. [Prediction of Future Observations in Growth Curve Models]: Comment. Statist. Sci., Volume 2, Number 4 (1987), 451--454.
  • See Comment: David Draper. [Prediction of Future Observations in Growth Curve Models]: Comment: On Exchangeability Judgments in Predictive Modeling and the Role of Data in Statistical Research. Statist. Sci., Volume 2, Number 4 (1987), 454--461.
  • See Comment: Alan Julian Izenman. [Prediction of Future Observations in Growth Curve Models]: Comment. Statist. Sci., Volume 2, Number 4 (1987), 461--463.
  • See Comment: Hirotugu Akaike. [Prediction of Future Observations in Growth Curve Models]: Comment. Statist. Sci., Volume 2, Number 4 (1987), 464--465.
  • See Comment: Seymour Geisser. [Prediction of Future Observations in Growth Curve Models]: Comment. Statist. Sci., Volume 2, Number 4 (1987), 465--467.
  • See Comment: C. Radhakrishna Rao. [Prediction of Future Observations in Growth Curve Models]: Rejoinder. Statist. Sci., Volume 2, Number 4 (1987), 467--471.